By Vincenzo Di Gennaro
We express a pointy Castelnuovo certain for the i-th plurigenus of a gentle number of given measurement n and measure d within the projective house P r , and classify the kinds achieving the sure, while n2, r2n+1, d>>r and i>>r. whilst n=2 and r=5, or n=3 and r=7, we provide an entire category, i.e. for any i1. sometimes, the kinds with maximal plurigenus aren't Castelnuovo kinds, i.e. types with maximal geometric genus. for instance, a Castelnuovo sort entire intersection on various measurement n+1 and minimum measure in P r , with r>(n 2 +3n)/(n-1), has no longer maximal i-th plurigenus, for i>>r. on account of the certain at the plurigenera, we receive an top certain for the self-intersection of the canonical package of a delicate projective type, whose canonical package deal is enormous and nef.
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A bound on the plurigenera of projective varieties by Vincenzo Di Gennaro